{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "be97ec9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e071f3a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .output_wrapper, .output {\n",
       "            height:auto !important;\n",
       "            max-height:100000px;\n",
       "        }\n",
       "        .output_scroll {\n",
       "            box-shadow:none !important;\n",
       "            webkit-box-shadow:none !important;\n",
       "        }\n",
       "        </style>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "786aa469",
   "metadata": {},
   "source": [
    "## Section3.1 Introduction\n",
    "\n",
    "上一章的最后讨论了离散贝叶斯滤波器的一些缺点。对于许多跟踪和滤波问题，我们希望有一个 **单峰 unimodal（最大似然估计）** 和 **连续 continuous** 的滤波器。也就是说，我们希望使用浮点数学（连续）对我们的系统进行建模，并且只表示一个信念（单峰）。例如，我们想说一架飞机在 (12.34, -95.54, 2389.5) 位置，即纬度、经度和高度。我们不希望我们的过滤器告诉我们“它可能在 (1.65, -78.01, 2100.45) 或者它可能在 (34.36, -98.23, 2543.79)。”这与我们对世界如何运作的物理直觉不符，正如我们所讨论的，计算多模式（多维）情况可能会非常昂贵。而且，当然，多个位置（多峰情况）估计使导航变得不可能。\n",
    "\n",
    "我们需要一种单峰、连续的方式来表示模拟现实世界如何运作的概率，并且计算效率高。高斯分布提供了所有这些特征。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3eab569",
   "metadata": {},
   "source": [
    "## Section3.2 Mean, Variance, and Standard Deviations\n",
    "\n",
    "你们中的大多数人都接触过数理统计，但请允许我介绍这些材料。 我要求你阅读这些材料，即使你确定你很了解它。 我问有两个原因。 首先，我想确保我们以相同的方式使用术语。 其次，致力于建立一种对数理统计的直观理解，这将在后面的章节中为您提供很好的帮助。 学习统计课程很容易，但是如果只记住公式和计算，可能对所学内容的含义感到困惑。\n",
    "\n",
    "### Section3.2.1 Random Variables\n",
    "\n",
    "每次您掷骰子时，*结果* 将在 1 到 6 之间。如果我们掷骰子一百万次，我们预测得到 （数字）1有1/6的次数。 因此，我们说结果为 1 的 *概率* 或 *比率* 是 1/6。 同样，如果我问你下一次掷骰结果的概率是 1，你会回答 1/6。\n",
    "\n",
    "这种值和相关概率的组合称为 [*随机变量*]（https://en.wikipedia.org/wiki/Random_variable）。 这里*随机*并不意味着过程是不确定的，只是我们缺乏关于结果的信息。 掷骰子的结果是有确定性的，但我们缺乏足够的信息来计算结果。 我们不知道会发生什么，除了概率。\n",
    "\n",
    "在我们定义术语时，值的范围称为 [*sample space（样本空间）*](https://en.wikipedia.org/wiki/Sample_space)。对于骰子，样本空间是 {1, 2, 3, 4, 5, 6}。对于硬币，样本空间是 {H, T}。 *空间*是一个数学术语，表示具有结构的集合。 骰子的样本空间是 1 到 6 范围内的自然数的子集。\n",
    "\n",
    "另一个随机变量的例子是大学学生的身高。 这里的样本空间是生物学定义的两个极限之间的实数范围。\n",
    "\n",
    "抛硬币和掷骰子等随机变量是*离散随机变量*。这意味着它们的样本空间由有限数量的值或可数无限数量的值（例如自然数）表示。人类的身高被称为*连续随机变量*，因为它们可以取两个极限之间的任何实数值。\n",
    "\n",
    "不要将随机变量的*测量*与实际值混淆。如果我们只能测量一个人的身高到 0.1 米，我们只能记录 0.1、0.2、0.3...2.7 的值，从而产生 27 个离散选择。尽管如此，一个人的身高可以在这些范围之间的任意实际值之间变化，因此身高是一个连续的随机变量。\n",
    "\n",
    "在统计学中，大写字母（capital letters）用于随机变量，通常来自字母表的后半部分。所以，我们可以说$X$是代表掷骰子的随机变量，或者$Y$是新生诗歌班学生的身高。后面的章节使用线性代数来解决这些问题，因此我们将遵循使用小写表示向量，使用大写表示矩阵的惯例。不幸的是，这些约定相互冲突，您必须从上下文中确定作者使用的是哪个。我总是对向量和矩阵使用粗体符号，这有助于区分两者。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a99ebb94",
   "metadata": {},
   "source": [
    "## Section3.3 Probability Distribution\n",
    "\n",
    "[*概率分布*](https://en.wikipedia.org/wiki/Probability_distribution) 给出了随机变量在样本空间中取任何值的概率。 例如，对于一个公平的六面骰子，我们可以说：\n",
    "\n",
    "|Value|Probability|\n",
    "|-----|-----------|\n",
    "|1|1/6|\n",
    "|2|1/6|\n",
    "|3|1/6|\n",
    "|4|1/6|\n",
    "|5|1/6|\n",
    "|6|1/6|\n",
    "\n",
    "我们用小写的 p 表示这个分布：$p(x)$。 使用普通的函数符号，我们会写：\n",
    "\n",
    "$$P(X{=}4) = p(4) = \\frac{1}{6}$$\n",
    "\n",
    "这表明骰子落在 4 上的概率是 $\\frac{1}{6}$。 $P(X{=}x_k)$ 是“$X$ 是 $x_k$ 的概率”的符号。 注意细微的符号差异。 大写的$P$表示单个事件的概率，小写的$p$是概率分布函数。 如果你不注意，这可能会让你误入歧途。 一些文本使用 $Pr$ 而不是 $P$ 来改善这一点。\n",
    "\n",
    "另一个例子是投掷硬币。 它有样本空间{H, T}。 硬币是公平的，所以正面 (H) 的概率是 50%，反面 (T) 的概率是 50%。 我们把它写成\n",
    "\n",
    "$$\\begin{gathered}P(X{=}H) = 0.5\\\\P(X{=}T)=0.5\\end{gathered}$$\n",
    "\n",
    "样本空间不是唯一的。一个骰子的样本空间是 {1, 2, 3, 4, 5, 6}。另一个有效的样本空间是{偶数（even），奇数（odd）}。另一个可能是{所有角落的点，而不是所有角落的点}。只要样本空间涵盖所有可能性，并且任何单个事件仅由一个元素描述，它就是有效的。 {even, 1, 3, 4, 5} 不是骰子的有效样本空间，因为值 4 与 'even' 和 '4' 都匹配。\n",
    "\n",
    "*离散随机值*的所有值的概率称为*离散概率分布*，*连续随机值*的所有值的概率称为*连续概率分布*。\n",
    "\n",
    "要成为概率分布，每个值 $x_i$ 的概率必须是 $x_i \\ge 0$，因为没有概率可以小于零。其次，所有值的概率之和必须等于 1。这对于抛硬币来说应该是直观的：如果正面的几率是 70%，那么反面的几率必须是 30%。我们将此要求表述为\n",
    "对于离散分布：\n",
    "\n",
    "$$\\sum\\limits_u P(X{=}u)= 1$$\n",
    "\n",
    "\n",
    "对于连续分布：\n",
    "\n",
    "$$\\int\\limits_u P(X{=}u) \\,du= 1$$\n",
    "\n",
    "。\n",
    "\n",
    "在上一章中，我们使用概率分布来估计狗在走廊中的位置。 例如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c88ed569",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sum =  1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import kf_book.book_plots as book_plots\n",
    "\n",
    "belief = np.array([1, 4, 2, 0, 8, 2, 2, 35, 4, 3, 2])\n",
    "belief = belief / np.sum(belief)\n",
    "with book_plots.figsize(y=2):\n",
    "    book_plots.bar_plot(belief)\n",
    "print('sum = ', np.sum(belief))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35a056d6",
   "metadata": {},
   "source": [
    "每个位置都有一个介于 0 和 1 之间的概率，并且所有位置的总和等于 1，因此这使其成为概率分布。 每个概率都是离散的，因此我们可以更准确地将其称为离散概率分布。 在实践中，我们省略了离散和连续这两个术语，除非我们有特定的理由进行区分。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f917d142",
   "metadata": {},
   "source": [
    "### Section3.3.1 The Mean, Median, and Mode of a Random Variable\n",
    "\n",
    "给定一组数据，我们经常想知道该组的代表值或平均值。 对此有很多衡量标准，这个概念被称为 [*中心趋势度量（measure of central tendency）*]（https://en.wikipedia.org/wiki/Central_tendency）。 例如，我们可能想知道班级中学生的*平均*身高。 我们都知道如何找到一组数据的平均值，但让我详细说明一下，以便我可以介绍更正式的符号和术语。 平均值的另一个词是 *mean*。 我们通过将值相加并除以值的数量来计算平均值。 如果学生的身高以米为单位\n",
    "\n",
    "$$X = \\{1.8, 2.0, 1.7, 1.9, 1.6\\}$$\n",
    "\n",
    "我们将平均值计算为\n",
    "\n",
    "$$\\mu = \\frac{1.8 + 2.0 + 1.7 + 1.9 + 1.6}{5} = 1.8$$\n",
    "\n",
    "传统上使用符号 $\\mu$ (mu) 来表示平均值。\n",
    "\n",
    "我们可以用等式形式化这个计算\n",
    "\n",
    "$$ \\mu = \\frac{1}{n}\\sum^n_{i=1} x_i$$\n",
    "\n",
    "NumPy 提供了`numpy.mean()` 来计算平均值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4dbb9d44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1.8, 2.0, 1.7, 1.9, 1.6]\n",
    "np.mean(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e99e7b9d",
   "metadata": {},
   "source": [
    "为方便起见，NumPy 数组提供了 `mean()` 方法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0f13df4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1.8, 2.0, 1.7, 1.9, 1.6])\n",
    "x.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ade4ed5",
   "metadata": {},
   "source": [
    "一组数字的 *mode* 是最常出现的数字。如果只有一个数字最常出现，我们说它是*unimodal 单峰*集合，如果两个或更多数字出现频率相同，则该集合是*mutilmodal 多峰*。例如集合 {1, 2, 2, 2, 3, 4, 4, 4} 有mode 2 和 4，这是mutilmodal的，集合 {5, 7, 7, 13} 有模式 7，它是单峰的。在本书中，我们不会以这种方式计算mode，但我们会在更一般的意义上使用单峰和多峰的概念。例如，在**离散贝叶斯**一章中，我们谈到了我们对狗的位置作为*多峰分布*的信念，因为我们为不同的位置分配了不同的概率。\n",
    "\n",
    "最后，一组数字的 *median* 是该组的中点，因此一半的值低于中位数，一半高于中位数。这里，上面和下面是关于被排序的集合。如果该集合包含偶数个值，则将中间的两个数字平均在一起。\n",
    "\n",
    "Numpy 提供 `numpy.median()` 来计算中位数。如您所见，{1.8, 2.0, 1.7, 1.9, 1.6} 的中位数为 1.8，因为 1.8 是该集合中排序后的第三个元素。在这种情况下，中位数等于平均值​​，但通常情况并非如此。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f1388d9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb6a3fe5",
   "metadata": {},
   "source": [
    "## Section 3.4: Expected Value of a Random Variable\n",
    "\n",
    "随机变量的 [*expected value（期望）*](https://en.wikipedia.org/wiki/Expected_value) 是如果我们取无限数量的样本然后将这些样本平均在一起时的平均值。 假设我们有 $x=[1,3,5]$ 并且每个值都是同样可能的。 我们 **期望** $x$ 的值是什么，是平均值吗？\n",
    "\n",
    "当然，这将是 1、3 和 5 的平均值，即 3。这应该是有道理的； 我们预计会出现相同数量的 1、3 和 5，因此 $(1+3+5)/3=3$ 显然是该无限系列样本的平均值。 换句话说，这里的期望值是样本空间的 *mean*。\n",
    "\n",
    "现在假设每个值都有不同的发生概率。 假设 1 有 80% 的机会发生，3 有 15% 的机会，而 5 只有 5% 的机会。 在这种情况下，我们通过将 $x$ 的每个值乘以它发生的百分比，并对结果求和来计算期望值。 对于这种情况，我们可以计算\n",
    "\n",
    "$$\\mathbb E[X] = (1)(0.8) + (3)(0.15) + (5)(0.05) = 1.5$$\n",
    "\n",
    "这里我介绍了 $x$ 的期望值的符号 $\\mathbb E[X]$。有些书籍或者文章中使用$E(x)$。 $x$ 的值 1.5 具有直观意义，因为 $x$ 为 1 的可能性远大于 3 或 5，并且 $x$ 为3 的可能性也比为 5大。\n",
    "\n",
    "$x_i$ 是$X$ 的$i^{th}$ （第 $i$ 个值），$p_i$ 是它发生的概率。 这给了我们\n",
    "\n",
    "\n",
    "$$\\mathbb E[X] = \\sum_{i=1}^n p_ix_i$$\n",
    "\n",
    "一个微不足道的代数公式表明，如果概率都相等，则期望值与平均值相同：\n",
    "\n",
    "$$\\mathbb E[X] = \\sum_{i=1}^n p_ix_i = \\frac{1}{n}\\sum_{i=1}^n x_i = \\mu_x$$\n",
    "\n",
    "如果 $x$ 是连续的，我们用积分代替求和:\n",
    "\n",
    "$$\\mathbb E[X] = \\int_{a}^b\\, xf(x) \\,dx$$\n",
    "\n",
    "其中 $f(x)$ 是 $x$ 的概率分布函数。 我们还不会使用这个等式，但我们将在下一章中使用它。\n",
    "\n",
    "我们可以写一点 Python 来模拟这个。 在这里，我取 1,000,000 个样本并计算我们刚刚分析计算的分布的期望值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6a113a98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4991"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total = 0\n",
    "N = 1000000\n",
    "for r in np.random.rand(N):\n",
    "    if r <= .80: total += 1\n",
    "    elif r < .95: total += 3\n",
    "    else: total += 5\n",
    "\n",
    "total / N"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0298bfa7",
   "metadata": {},
   "source": [
    "您可以看到计算值接近解析得出的值。 这并不准确，因为获得准确的值需要无限的样本量。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ebc8207",
   "metadata": {},
   "source": [
    "### Section 3.4.1 Exercise\n",
    "\n",
    "掷骰子的期望值是多少？\n",
    "\n",
    "### Solution\n",
    "\n",
    "每一面的可能性相等，所以每一面的概率都是 1/6。 因此\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbb E[X] &= 1/6\\times1 + 1/6\\times 2 + 1/6\\times 3 + 1/6\\times 4 + 1/6\\times 5 + 1/6\\times6 \\\\\n",
    "&= 1/6(1+2+3+4+5+6)\\\\&= 3.5\\end{aligned}$$\n",
    "\n",
    "### Exercise\n",
    "\n",
    "给定均匀连续分布(的概率密度函数)\n",
    "\n",
    "$$f(x) = \\frac{1}{b - a}$$\n",
    "\n",
    "当 $a=0$ 和 $b=20$ 时计算期望值。\n",
    "\n",
    "### Solution\n",
    "$$\\begin{aligned}\n",
    "\\mathbb E[X] &= \\int_0^{20}\\, x\\frac{1}{20} \\,dx \\\\\n",
    "&= \\bigg[\\frac{x^2}{40}\\bigg]_0^{20} \\\\\n",
    "&= 10 - 0 \\\\\n",
    "&= 10\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51d7dd3a",
   "metadata": {},
   "source": [
    "### Section 3.4.5： Variance of a Random Variable\n",
    "\n",
    "上面的计算告诉我们学生的平均身高，但它并没有告诉我们我们可能想知道的一切。 例如，假设我们有三个班级的学生，我们将其标记为 $X$、$Y$ 和 $Z$，其高度如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c7cd938c",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [1.8, 2.0, 1.7, 1.9, 1.6]\n",
    "Y = [2.2, 1.5, 2.3, 1.7, 1.3]\n",
    "Z = [1.8, 1.8, 1.8, 1.8, 1.8]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0cadbd9",
   "metadata": {},
   "source": [
    "使用 NumPy，我们看到每个类的平均高度是相同的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8b64f4fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.8 1.8 1.8\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(X), np.mean(Y), np.mean(Z))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1cb3ee5",
   "metadata": {},
   "source": [
    "\n",
    "每个班级（学生）的平均值为 1.8 米，但请注意，第二个班级的高度变化量比第一个班级大得多，而第三个班级则完全没有变化。\n",
    "\n",
    "平均值告诉我们一些关于数据的信息，但不是全部。 我们希望能够指定学生的身高之间有多少 *variation*。 你可以想象这有很多原因。 也许一个学区需要订购 5,000 张课桌，并且他们希望确保购买适合学生身高范围的尺寸。\n",
    "\n",
    "统计学已经将这种测量变化的概念正式化为 [*标准差（standard deviation）*](https://en.wikipedia.org/wiki/Standard_deviation) 和 [*方差（variance）*](https://en.wikipedia.org/ 维基/方差）。 计算方差的方程是\n",
    "\n",
    "$$\\mathit{VAR}(X) = \\mathbb  E[(X - \\mu)^2]$$\n",
    "\n",
    "暂时忽略平方，您可以看到方差是样本空间 $X$ 与均值 $\\mu:$ ($X-\\mu)$ 之间的*期望（expected value）*。 稍后我将解释平方项的用途。 期望值的公式是 $\\mathbb E[X] = \\sum\\limits_{i=1}^n p_ix_i$ 所以我们可以把它代入上面的等式得到\n",
    "\n",
    "$$\\mathit{VAR}(X) = \\frac{1}{n}\\sum_{i=1}^n (x_i - \\mu)^2$$\n",
    " \n",
    "让我们计算三个类的方差，看看我们得到什么值并熟悉这个概念。\n",
    "\n",
    "$X$ 的平均值是 1.8 ($\\mu_x = 1.8$) 所以我们计算\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\mathit{VAR}(X) &=\\frac{(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2} {5} \\\\\n",
    "&= \\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5} \\\\\n",
    "\\mathit{VAR}(X)&= 0.02 \\, m^2\n",
    "\\end{aligned}$$\n",
    "\n",
    "NumPy 提供了函数 var() 来计算方差："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a9347675",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.02 meters squared\n"
     ]
    }
   ],
   "source": [
    "print(f\"{np.var(X):.2f} meters squared\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88a1a0b4",
   "metadata": {},
   "source": [
    "这可能有点难以解释。 高度以米为单位，但方差为米的平方。 因此，我们有一个更常用的度量标准，即*标准差*，它定义为方差的平方根：\n",
    "\n",
    "$$\\sigma = \\sqrt{\\mathit{VAR}(X)}=\\sqrt{\\frac{1}{n}\\sum_{i=1}^n(x_i - \\mu)^2}$$\n",
    "\n",
    "通常使用 $\\sigma$ 作为*标准差*，使用 $\\sigma^2$ 作为*方差*。 在本书的大部分内容中，我将使用 $\\sigma^2$ 而不是 $\\mathit{VAR}(X)$ 来表示方差； 它们表示同样的东西。\n",
    "\n",
    "对于第一个班级，我们计算标准差\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_x &=\\sqrt{\\frac{(1.8-1.8)^2 + (2-1.8)^2 + (1.7-1.8)^2 + (1.9-1.8)^2 + (1.6-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0 + 0.04 + 0.01 + 0.01 + 0.04}{5}} \\\\\n",
    "\\sigma_x&= 0.1414\n",
    "\\end{aligned}$$\n",
    "\n",
    "我们可以使用计算标准差的 NumPy 方法“numpy.std()”来验证这个计算。 “std”是标准差的常用缩写。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "36b7f7d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std 0.1414\n",
      "var 0.0200\n"
     ]
    }
   ],
   "source": [
    "print(f\"std {np.std(X):.4f}\")\n",
    "print(f\"var {np.std(X)**2:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20d7c5aa",
   "metadata": {},
   "source": [
    "当然，$0.1414^2 = 0.02$，这与我们之前对方差的计算一致。\n",
    "\n",
    "标准差意味着什么？ 它告诉我们它们之间的高度差异有多大。 “多少（原文中代表前一句的How much）”不是一个数学术语。 一旦我们在下一节中介绍了高斯的概念，我们将能够更精确地定义它。 现在我要说的是，对于许多事情来说，所有值的 68% 位于平均值的一个标准差内。 换句话说，我们可以得出结论，对于随机班级，68% 的学生身高在 1.66 (1.8-0.1414) 米和 1.94 (1.8+0.1414) 米之间。\n",
    "\n",
    "**注：概率论中的3 $\\sigma$ 原则**\n",
    "\n",
    "我们可以在图中查看："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b988ef79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.gaussian_internal import plot_height_std\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plot_height_std(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18e6bd4a",
   "metadata": {},
   "source": [
    "对于只有 5 名学生，我们显然不会在一个标准差内准确地得到 68%。 我们确实看到 5 个学生中有 3 个在 $\\pm1\\sigma$ 以内，即 60%，这与仅使用 5 个样本可以达到的 68% 非常接近。 让我们看看一个有 100 名学生的班级的结果。\n",
    "\n",
    "> 我们把一个标准差写成$1\\sigma$，读作“one standard deviation”，而不是“one sigma”。 两个标准差是 $2\\sigma$，以此类推。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "587a2a18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 1.812\n",
      "std  = 0.140\n"
     ]
    }
   ],
   "source": [
    "from numpy.random import randn\n",
    "data = 1.8 + randn(100)*.1414\n",
    "mean, std = data.mean(), data.std()\n",
    "\n",
    "plot_height_std(data, lw=2)\n",
    "print(f'mean = {mean:.3f}')\n",
    "print(f'std  = {std:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "575e0c6c",
   "metadata": {},
   "source": [
    "肉眼看来，大约 68% 的高度位于平均值 1.8 的 $\\pm1\\sigma$ 之内，但我们可以用代码验证这一点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c8a34257",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum((data > mean-std) & (data < mean+std)) / len(data) * 100."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17e45596",
   "metadata": {},
   "source": [
    "我们将很快更深入地讨论这个问题。 现在让我们计算标准差\n",
    "\n",
    "$$Y = [2.2, 1.5, 2.3, 1.7, 1.3]$$\n",
    "\n",
    "$Y$ 的均值是 $\\mu=1.8$ m，所以\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_y &=\\sqrt{\\frac{(2.2-1.8)^2 + (1.5-1.8)^2 + (2.3-1.8)^2 + (1.7-1.8)^2 + (1.3-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{0.152} = 0.39 \\ m\n",
    "\\end{aligned}$$\n",
    "\n",
    "我们将使用 NumPy 验证这一点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "779912f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std of Y is 0.39 m\n"
     ]
    }
   ],
   "source": [
    "print(f'std of Y is {np.std(Y):.2f} m')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14e4e4f0",
   "metadata": {},
   "source": [
    "这符合我们的预期。 $Y$ 的高度变化更大，标准差也更大。\n",
    "\n",
    "最后，让我们计算 $Z$ 的标准差。 值没有变化，因此我们预计标准偏差为零。\n",
    "\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\sigma_z &=\\sqrt{\\frac{(1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2 + (1.8-1.8)^2} {5}} \\\\\n",
    "&= \\sqrt{\\frac{0+0+0+0+0}{5}} \\\\\n",
    "\\sigma_z&= 0.0 \\ m\n",
    "\\end{aligned}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c62cf058",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "print(np.std(Z))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bf94523",
   "metadata": {},
   "source": [
    "在我们继续之前，我需要指出，我忽略了平均而言男性比女性高（这一事实）。通常，仅包含男性或女性的班级的身高差异将小于具有两性的班级。对于其他因素也是如此。营养良好的儿童比营养不良的儿童高。斯堪的纳维亚人比意大利人高。在设计实验时，统计学家需要考虑这些因素。\n",
    "\n",
    "我建议我们可能会执行此分析以订购学区的课桌。对于每个年龄组，可能有两种不同的平均值 - 一个聚集在女性的平均身高周围，第二个平均值聚集在男性的平均身高周围。整个班级的平均值将介于两者之间。如果我们为所有学生的平均水平购买课桌，我们最终可能会得到一个既不适合学校男生也不适合女生的课桌！\n",
    "\n",
    "我们不会在本书中考虑这些问题。如果您需要学习处理这些问题的技术，请查阅任何标准概率书籍。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91d6453a",
   "metadata": {},
   "source": [
    "### Why the Square of the Differences\n",
    "\n",
    "\n",
    "为什么我们要取方差的*平方*？ 我可以研究很多数学，但让我们以一种简单的方式来看待这个问题。 这是 $X$ 的值相对于 $X=[3,-3,3,-3]$ 的平均值绘制的图表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "749f22e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAusAAAFMCAYAAAByCPL2AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAVuElEQVR4nO3dXYyUZ9348d8iwyxrmd1lgXb7MFQoUXxDDVYEjQHtVkiscmAfj2wxpAdNaVIhRnpgmz1oVhIOatIGazTigU3qG5qQtHXS3dKYiLYkTdRQEppWGtiWusRZ3H12GNl5Dhr2gf++zfD3Zq7dfj4JyczszVxXk1+ufnt3drelVqvVAgAASM6CZm8AAACYmlgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABI1MJmb2Am4+Pjcfbs2ViyZEm0tLQ0ezsAAPAfUavV4sKFC3HzzTfHggXT3z9POtbPnj0bxWKx2dsAAIBMvPnmm7Fy5cppv550rC9ZsiQiIl5//fVYunRpk3dD6qrVavz+97+PO+64I3K5XLO3Q8LMCo0wL9TLrNCI8+fPx+rVqyd6dzpJx/rlj74sWbIkCoVCk3dD6qrVarS1tUWhUHBIMiOzQiPMC/UyKzSiWq1GRMz6UW/fYAoAAIkS6wAAkCixDgAAiRLrAACQKLEOAACJEusAAJAosQ4AAInKNNYPHjwY69evj0KhEIVCITZt2hTPPPNMlksCAMC8kWmsr1y5Mr7//e/H8ePH4+WXX44vfvGL8bWvfS3+9re/ZbksAADMC5n+BtM777zzquePPvpoHDx4MI4dOxYf/ehHs1ya95harRYjIyMxNjYWtVqt2dsB5glnC9Bsmcb6lS5duhS//OUvY2RkJDZt2jTlNZVKJSqVysTz4eHhiHj317Fe/pWsMJWRkZHo7OyMiIhz585FR0dHczdE0i6fJ84VZuNsoRHOFhpR75xkHut/+ctfYtOmTTE2NhY33HBDHD58OD7ykY9MeW1fX1/09vZOen1gYCDa2tqy3ipz2NjY2MTj/v7+aG1tbeJumCtKpVKzt0DinC1cC2cL9RgdHa3rupZaxv9f7+LFi3H69Okol8vxq1/9Kn784x/H0aNHpwz2qe6sF4vFGBwcjK6uriy3yRzn7heNqFarUSqVoqenJ3K5XLO3Q8KcLTTC2UIjhoaGoru7O8rlchQKhWmvy/zO+qJFi2Lt2rUREbFhw4Z46aWX4gc/+EE8+eSTk67N5/ORz+cnvZ7L5Qw9M7pyPswL9TIrzMbZwrUwK9Sj3hm57j9nfXx8/Kq75wAAwNQyvbP+0EMPxfbt22PVqlVx4cKFeOqpp+KFF16I5557LstlAQBgXsg01s+dOxd33313DA4ORnt7e6xfvz6ee+656OnpyXJZAACYFzKN9Z/85CdZvj0AAMxr1/0z6wAAQH3EOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACQq01jv6+uL2267LZYsWRIrVqyIHTt2xMmTJ7NcEgAA5o1MY/3o0aNx//33x7Fjx6JUKkW1Wo077rgjRkZGslwWAADmhYVZvvmzzz571fNDhw7FihUr4vjx4/GFL3why6UBAGDOyzTW/1/lcjkiIpYuXTrl1yuVSlQqlYnnw8PDERFRrVajWq1mv0HmrCvnw7wwm8vzYU6YjbOFRjhbaES9c3LdYn18fDwefPDB+NznPhcf+9jHprymr68vent7J70+MDAQbW1tWW+ROWxsbGzicX9/f7S2tjZxN8wVpVKp2Vsgcc4WroWzhXqMjo7WdV1LrVarZbyXiIi477774plnnok//OEPsXLlyimvmerOerFYjMHBwejq6roe22SOGhkZic7OzoiIOHfuXHR0dDR3QyStWq1GqVSKnp6eyOVyzd4OCXO20AhnC40YGhqK7u7uKJfLUSgUpr3uutxZ3717dxw5ciRefPHFaUM9IiKfz0c+n5/0ei6XM/TM6Mr5MC/Uy6wwG2cL18KsUI96ZyTTWK/VavHAAw/E4cOH44UXXojVq1dnuRwAAMwrmcb6/fffH0899VT87ne/iyVLlsRbb70VERHt7e2xePHiLJcGAIA5L9Ofs37w4MEol8uxZcuW6O7unvjz9NNPZ7ksAADMC5l/DAYAALg2md5ZBwAArp1YBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgERlGusvvvhi3HnnnXHzzTdHS0tL/Pa3v81yOQAAmFcyjfWRkZH4xCc+EU888USWywAAwLy0MMs33759e2zfvr3u6yuVSlQqlYnnw8PDERFRrVajWq3+x/fH/HHlfJgXZnN5PswJs3G20AhnC42od04yjfVG9fX1RW9v76TXBwYGoq2trQk7Yq4YGxubeNzf3x+tra1N3A1zRalUavYWSJyzhWvhbKEeo6OjdV3XUqvVahnv5d2FWlri8OHDsWPHjmmvmerOerFYjMHBwejq6roOu2SuGhkZic7OzoiIOHfuXHR0dDR3QyStWq1GqVSKnp6eyOVyzd4OCXO20AhnC40YGhqK7u7uKJfLUSgUpr0uqTvr+Xw+8vn8pNdzuZyhZ0ZXzod5oV5mhdk4W7gWZoV61DsjfnQjAAAkSqwDAECiMv0YzL/+9a84derUxPPXX389XnnllVi6dGmsWrUqy6UBAGDOyzTWX3755di6devE8z179kRExD333BOHDh3KcmkAAJjzMo31LVu2xHX6YTMAADDv+Mw6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAoq5LrD/xxBPxgQ98IFpbW2Pjxo3x5z//+XosCwAAc9rCrBd4+umnY8+ePfHDH/4wNm7cGI899lh8+ctfjpMnT8aKFSvqeo/Ri/+OxRf/nfFOmctGL16Kllw+IiL+5+KlWGRemEatVovh8nAMj4zFSOXfsajW0uwtkTBnC/VyttCo0TrPk5ZarVbLciMbN26M2267LR5//PGIiBgfH49isRgPPPBA7Nu376prK5VKVCqViefDw8NRLBaj+OAvYkG+LcttAgDAdTNeGY03H/vvKJfLUSgUpr0u04/BXLx4MY4fPx633377/y24YEHcfvvt8cc//nHS9X19fdHe3j7xp1gsZrk9AABIWqYfg/nHP/4Rly5dihtvvPGq12+88cZ49dVXJ13/0EMPxZ49eyaeX76zfvTbm2Np19Ist8ocV6tFDA+X4+gLR2Pb9u2xaFGu2VsiUaMjo/FfK/8rIiLeeOONaG9vb/KOSJmzhXo5W2jU+aHzseax2a/L/DPrjcjn85HP5ye9Xnh/a7S/f3ETdsRc8v78wii8vzU6blgcuZx/oTK1hTEeteq7H7crtDlbmJ2zhXo4W2jUv8da67ou04/BLFu2LN73vvfF22+/fdXrb7/9dtx0001ZLg0AAHNeprG+aNGi2LBhQzz//PMTr42Pj8fzzz8fmzZtynJpAACY8zL/GMyePXvinnvuiU9/+tPxmc98Jh577LEYGRmJb33rW1kvDQAAc1rmsf6Nb3wj3nnnnXj44Yfjrbfeik9+8pPx7LPPTvqmUwAA4GrX5RtMd+/eHbt3774eSwEAwLyR6WfWAQCAayfWAQAgUWIdAAASJdYBACBRYh0AABIl1gEAIFFiHQAAEiXWAQAgUWIdAAASJdYBACBRYh0AABIl1gEAIFFiHQAAEiXWAQAgUWIdAAASJdYBACBRYh0AABIl1gEAIFFiHQAAEiXWAQAgUWIdAAASJdYBACBRYh0AABIl1gEAIFFiHQAAEiXWAQAgUWIdAAASJdYBACBRYh0AABIl1gEAIFFiHQAAEiXWAQAgUWIdAAASJdYBACBRYh0AABKVWaw/+uijsXnz5mhra4uOjo6slgEAgHkrs1i/ePFi3HXXXXHfffdltQQAAMxrC7N6497e3oiIOHToUFZLAADAvJZZrF+LSqUSlUpl4vnw8HBERFSr1ahWq83aFnPE5RkxK8zkyvlwtlAPZwv1cLbQqHpnJKlY7+vrm7gjf6WBgYFoa2trwo6Yi0qlUrO3QMLGxsYmHvf390dra2sTd8Nc4mxhJs4WGjU6OlrXdS21Wq1W75vu27cv9u/fP+M1J06ciHXr1k08P3ToUDz44IPxz3/+c9b3n+rOerFYjMHBwejq6qp3m7xHVavVKJVK0dPTE7lcrtnbIVEjIyPR2dkZERHnzp3zDfDMytlCPZwtNGpoaCi6u7ujXC5HoVCY9rqG7qzv3bs3du7cOeM1a9asaeQtr5LP5yOfz096PZfLOSCpm3lhJlfOhlmhEeaFmThbaFS9M9JQrC9fvjyWL19+TRsCAAAak9ln1k+fPh3nz5+P06dPx6VLl+KVV16JiIi1a9fGDTfckNWyAAAwb2QW6w8//HD87Gc/m3j+qU99KiLe/WbRLVu2ZLUsAADMG5n9UqRDhw5FrVab9EeoAwBAfTKLdQAA4P+PWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEiXUAAEiUWAcAgESJdQAASJRYBwCARIl1AABIlFgHAIBEZRbrb7zxRuzatStWr14dixcvjltvvTUeeeSRuHjxYlZLAgDAvLIwqzd+9dVXY3x8PJ588slYu3Zt/PWvf4177703RkZG4sCBA1ktCwAA80Zmsb5t27bYtm3bxPM1a9bEyZMn4+DBg9PGeqVSiUqlMvF8eHg4IiKq1WpUq9Wstso8cXlGzAozuXI+nC3Uw9lCPZwtNKreGcks1qdSLpdj6dKl0369r68vent7J70+MDAQbW1tWW6NeaRUKjV7CyRsbGxs4nF/f3+0trY2cTfMJc4WZuJsoVGjo6N1XddSq9VqGe8lIiJOnToVGzZsiAMHDsS999475TVT3VkvFosxODgYXV1d12ObzGHVajVKpVL09PRELpdr9nZI1MjISHR2dkZExLlz56Kjo6O5GyJ5zhbq4WyhUUNDQ9Hd3R3lcjkKhcK01zV8Z33fvn2xf//+Ga85ceJErFu3buL5mTNnYtu2bXHXXXdNG+oREfl8PvL5/KTXc7mcA5K6mRdmcuVsmBUaYV6YibOFRtU7Iw3H+t69e2Pnzp0zXrNmzZqJx2fPno2tW7fG5s2b40c/+lGjywEAwHtWw7G+fPnyWL58eV3XnjlzJrZu3RobNmyIn/70p7FggR/rDgAA9crsG0zPnDkTW7ZsiVtuuSUOHDgQ77zzzsTXbrrppqyWBQCAeSOzWC+VSnHq1Kk4depUrFy58qqvXafvaQUAgDkts8+l7Ny5M2q12pR/AACA2fkQOQAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKLEOgAAJEqsAwBAosQ6AAAkSqwDAECixDoAACRKrAMAQKIyjfWvfvWrsWrVqmhtbY3u7u745je/GWfPns1ySQAAmDcyjfWtW7fGL37xizh58mT8+te/jtdeey2+/vWvZ7kkAADMGwuzfPNvf/vbE49vueWW2LdvX+zYsSOq1WrkcrlJ11cqlahUKhPPh4eHIyKiWq1GtVrNcqvMA5dnxKwwkyvnw9lCPZwt1MPZQqPqnZFMY/1K58+fj5///OexefPmKUM9IqKvry96e3snvT4wMBBtbW1Zb5F5olQqNXsLJGxsbGzicX9/f7S2tjZxN8wlzhZm4myhUaOjo3Vd11Kr1WpZbuS73/1uPP744zE6Ohqf/exn48iRI9HV1TXltVPdWS8WizE4ODjt34HLqtVqlEql6OnpmfY/CKFWq0W5XI7+/v74yle+EosWLWr2lkics4V6OFto1NDQUHR3d0e5XI5CoTDtdQ3fWd+3b1/s379/xmtOnDgR69ati4iI73znO7Fr1674+9//Hr29vXH33XfHkSNHoqWlZdLfy+fzkc/nJ72ey+UckNTNvDCbjo6OaG1tjUWLFpkV6uZsYTbOFhpR74w0HOt79+6NnTt3znjNmjVrJh4vW7Ysli1bFh/84Afjwx/+cBSLxTh27Fhs2rSp0aUBAOA9peFYX758eSxfvvyaFhsfH4+IuOqjLgAAwNQy+wbTP/3pT/HSSy/F5z//+ejs7IzXXnstvve978Wtt97qrjoAANQhs5+z3tbWFr/5zW/iS1/6UnzoQx+KXbt2xfr16+Po0aNTfi4dAAC4WmZ31j/+8Y9Hf39/Vm8PAADzXqa/wRQAALh2Yh0AABIl1gEAIFFiHQAAEiXWAQAgUZn9NJj/hFqtFhERFy5c8Gt7mVW1Wo3R0dEYHh42L8zIrNAI80K9zAqNuHDhQkT8X+9OJ+lYHxoaioiI1atXN3knAADwnzc0NBTt7e3Tfj3pWF+6dGlERJw+fXrGfwiIiBgeHo5isRhvvvlmFAqFZm+HhJkVGmFeqJdZoRHlcjlWrVo10bvTSTrWFyx49yP17e3thp66FQoF80JdzAqNMC/Uy6zQiMu9O+3Xr9M+AACABol1AABIVNKxns/n45FHHol8Pt/srTAHmBfqZVZohHmhXmaFRtQ7Ly212X5eDAAA0BRJ31kHAID3MrEOAACJEusAAJAosQ4AAIkS6wAAkCixDgAAiRLrAACQKLEOAACJ+l+bZCJyJcuNhAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = [3, -3, 3, -3]\n",
    "mean = np.average(X)\n",
    "for i in range(len(X)):\n",
    "    plt.plot([i ,i], [mean, X[i]], color='k')\n",
    "plt.axhline(mean)\n",
    "plt.xlim(-1, len(X))\n",
    "plt.tick_params(axis='x', labelbottom=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b06e99e2",
   "metadata": {},
   "source": [
    "如果我们不取差异的平方，则符号（数据的正负号）将抵消一切：\n",
    "\n",
    "$$\\frac{(3-0) + (-3-0) + (3-0) + (-3-0)}{4} = 0$$\n",
    "\n",
    "这显然是不正确的，因为数据中的方差大于 0。\n",
    "\n",
    "也许我们可以使用绝对值？ 我们可以通过检查看到结果是 $12/4=3$，这当然是正确的——每个值与平均值相差 3。 但是如果我们有 $Y=[6, -2, -3, 1]$ 呢？ 在这种情况下，我们得到 $12/4=3$。 $Y$ 显然比 $X$ 更分散，但计算产生相同的方差。 如果我们使用平方公式，我们得到 $Y$ 的方差为 3.5，这反映了它更大的变化。\n",
    "\n",
    "这不是正确性的证明。 事实上，这项技术的发明者卡尔·弗里德里希·高斯认识到它有些武断。 如果存在异常值，则对差异进行平方会对该项赋予不成比例的权重。 例如，让我们看看如果我们有会发生什么："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2ec86b5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance of X with outlier    = 621.45\n",
      "Variance of X without outlier =   2.03\n"
     ]
    }
   ],
   "source": [
    "X = [1, -1, 1, -2, -1, 2, 1, 2, -1, 1, -1, 2, 1, -2, 100]\n",
    "print(f'Variance of X with outlier    = {np.var(X):6.2f}')\n",
    "print(f'Variance of X without outlier = {np.var(X[:-1]):6.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8da57893",
   "metadata": {},
   "source": [
    "这个对吗”？你告诉我。没有异常值100时，我们可以获得 $\\sigma^2=2.03$，它准确地反映了 $X$ 在没有异常值的情况下是如何变化的。一个异常值淹没了方差计算。我们是否想要淹没计算以便我们知道存在异常值，或者稳健地合并异常值并且仍然提供接近没有异常值的值的估计？再说一次，你告诉我。显然，这取决于你的问题。\n",
    "\n",
    "我不会继续走这条路；如果你有兴趣，你可能想看看 James Berger 在这个问题上所做的工作，在一个名为 *Bayesian robustness* 的领域，或 Peter J. Huber [4] 的 *robust statistics* 的优秀出版物。在本书中，我们将始终使用高斯定义的方差和标准差。\n",
    "\n",
    "从中收集的要点是，这些 *摘要统计（summary statistics）* 数据总是讲述关于我们数据的不完整故事。在这个例子中，高斯定义的方差并没有告诉我们我们有一个大的异常值。然而，它是一个强大的工具，因为我们可以用几个数字简洁地描述一个大数据集。如果我们有 10 亿个数据点，我们就不想用肉眼检查图或查看数字列表；摘要统计为我们提供了一种以有用的方式描述数据形状的方法。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c64f3c6",
   "metadata": {},
   "source": [
    "## Gaussians\n",
    "\n",
    "我们现在准备好了解 [Gaussians](https://en.wikipedia.org/wiki/Gaussian_function)。 让我们提醒自己本章的动机。\n",
    "\n",
    "> 我们需要一种可以模拟真实世界运行模式，且高计算效率的单峰、连续的概率表示方式。\n",
    "\n",
    "让我们看一下高斯分布图，以了解我们在说什么。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f56d9757",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.stats import plot_gaussian_pdf\n",
    "plot_gaussian_pdf(mean=1.8, variance=0.1414**2, \n",
    "                  xlabel='Student Height', ylabel='pdf');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b342432",
   "metadata": {},
   "source": [
    "这条曲线是一个[*概率密度函数（probability density function）*]（https://en.wikipedia.org/wiki/Probability_density_function）或简称*pdf*。 它显示了随机变量取值的相对可能性（后面的例子可以很好有助于理解这个相对性）。 我们可以从图表中看出，学生在 1.8 m 附近的身高比 1.7 m 高一些，1.9 m 对 1.4 m 的身高更有可能。 换句话说，很多学生的身高会接近1.8m，很少有学生的身高会达到1.4m或2.2米。 最后，请注意曲线以 1.8 m 的平均值为中心。\n",
    "\n",
    "> 我在 Notebook *Computing_and_Plotting_PDFs* 的\n",
    "Supporting_Notebooks 文件夹。 您可以在线阅读 [这里](https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb) [1]。\n",
    "\n",
    "您可能会将其识别为“钟形曲线”。 这条曲线无处不在，因为在现实世界条件下，许多观察结果都以这种方式分布。 我不会使用术语“钟形曲线”来指代高斯，因为许多概率分布具有相似的钟形曲线形状。 非数学来源可能不那么精确，所以当你看到没有定义使用的术语时，要谨慎地得出结论。\n",
    "\n",
    "这条曲线并不是高度所独有的——大量的自然现象都表现出这种分布，包括我们在滤波问题中使用的传感器。 正如我们将看到的，它还具有我们正在寻找的所有属性——它代表一个单峰信念或概率值，它是连续的，并且计算效率高。 我们很快就会发现它还具有其他我们可能没有意识到我们想要的特征。\n",
    "\n",
    "为了进一步激励你，回忆一下*离散贝叶斯*一章中概率分布的形状："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "983f49ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.book_plots as book_plots\n",
    "belief = [0., 0., 0., 0.1, 0.15, 0.5, 0.2, .15, 0, 0]\n",
    "book_plots.bar_plot(belief)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5531a64",
   "metadata": {},
   "source": [
    "它们不是完美的高斯曲线，但它们是相似的。 我们将使用高斯来代替那章中使用的离散概率！"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8762f5d",
   "metadata": {},
   "source": [
    "## Section 3.6： Nomenclature\n",
    "\n",
    "在继续介绍一些新术语之前 - 本节描述的*随机变量*的*概率密度*，其值介于 ($-\\infty..\\infty)$ 之间。 这意味着什么？ 想象一下，我们对一段高速公路上的汽车速度进行了无数次无限精确的测量。 然后，我们可以通过显示以任何给定速度经过的汽车的相对数量来绘制结果。 如果平均值为 120 公里/小时，它可能如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "46ddb7e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_gaussian_pdf(mean=120, variance=17**2, xlabel='speed(kph)');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b05f3275",
   "metadata": {},
   "source": [
    "y 轴描绘了*概率密度*——在相应 x 轴上显示了对应车辆的速度（意译）。我将在下一节中进一步解释这一点。\n",
    "\n",
    "高斯模型并不完美。尽管这些图表没有显示它，但分布的 *tails* 延伸到无穷大。 *尾巴*是曲线的远端，值最低。当然，人的身高或汽车速度不能小于零，更不用说 $-\\infty$ 或 $\\infty$。 “The map is not the territory 地图不是领土”是一种常见的表达方式，对于贝叶斯滤波和统计而言也是如此。上面的高斯分布模拟了测量的汽车速度的分布，但作为一个模型，它必然是不完美的。模型和现实之间的差异将在这些滤波器中一次又一次地出现。高斯被用于许多数学分支，不是因为它们完美地模拟了现实，而是因为它们比任何其他相对准确的选择更容易使用。然而，即使在本书中，高斯也无法模拟现实，迫使我们使用计算成本高的替代方案。\n",
    "\n",
    "您将听到这些分布称为*高斯分布*或*正态分布*。 *Gaussian* 和 *normal* 在此上下文中的含义相同，并且可以互换使用。我将在本书中同时使用这两个术语，因为不同的来源会使用这两个术语，我希望你习惯于同时看到这两个术语。最后，就像在本段中一样，通常会缩短名称并谈论 *Gaussian* 或 *normal*——这些都是 *Gaussian 分布*的典型快捷名称。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc4ab397",
   "metadata": {},
   "source": [
    "## Section 3.7： Gaussian Distributions\n",
    "\n",
    "让我们探索高斯是如何工作的。 高斯是一个*连续概率分布*，它完全用两个参数来描述，均值 ($\\mu$) 和方差 ($\\sigma^2$)。 它被定义为：\n",
    "\n",
    "$$ \n",
    "f(x, \\mu, \\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\big [{-\\frac{(x-\\mu)^2}{2\\sigma^2} }\\big ]\n",
    "$$\n",
    "\n",
    "$\\exp[x]$ 是 $e^x$ 的符号。\n",
    "\n",
    "<p> 如果你以前没有见过这个等式，不要被它吓倒； 你不需要记住或操纵它。 该函数的计算存储在 stats.py 中，函数为 gaussian(x, mean, var, normed=True)。\n",
    "    \n",
    "去掉常数，你可以看到它是一个简单的指数：\n",
    "    \n",
    "$$f(x)\\propto e^{-x^2}$$\n",
    "\n",
    "具有熟悉的钟形曲线形状"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9a50feb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-3, 3, .01)\n",
    "plt.plot(x, np.exp(-x**2));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84906ff6",
   "metadata": {},
   "source": [
    "让我们提醒自己如何查看函数的代码。 在单元格中，键入函数名称，后跟两个问号，然后按 CTRL+ENTER。 这将打开一个显示源的弹出窗口。 取消注释下一个单元格并立即尝试。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e4030f68",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[1;31mSignature:\u001b[0m \u001b[0mgaussian\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnormed\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mSource:\u001b[0m   \n",
      "\u001b[1;32mdef\u001b[0m \u001b[0mgaussian\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvar\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnormed\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[1;34m\"\"\"\n",
      "    returns normal distribution (pdf) for x given a Gaussian with the\n",
      "    specified mean and variance. All must be scalars.\n",
      "\n",
      "    gaussian (1,2,3) is equivalent to scipy.stats.norm(2,math.sqrt(3)).pdf(1)\n",
      "    It is quite a bit faster albeit much less flexible than the latter.\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "\n",
      "    x : scalar or array-like\n",
      "        The value for which we compute the probability\n",
      "\n",
      "    mean : scalar\n",
      "        Mean of the Gaussian\n",
      "\n",
      "    var : scalar\n",
      "        Variance of the Gaussian\n",
      "\n",
      "    norm : bool, default True\n",
      "        Normalize the output if the input is an array of values.\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "\n",
      "    probability : float\n",
      "        probability of x for the Gaussian (mean, var). E.g. 0.101 denotes\n",
      "        10.1%.\n",
      "\n",
      "    Examples\n",
      "    --------\n",
      "\n",
      "    >>> gaussian(8, 1, 2)\n",
      "    1.3498566943461957e-06\n",
      "\n",
      "    >>> gaussian([8, 7, 9], 1, 2)\n",
      "    array([1.34985669e-06, 3.48132630e-05, 3.17455867e-08])\n",
      "    \"\"\"\u001b[0m\u001b[1;33m\n",
      "\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[0mg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpi\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mvar\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m.5\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mmean\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2.\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mvar\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[1;32mif\u001b[0m \u001b[0mnormed\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\n",
      "\u001b[0m        \u001b[0mg\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mg\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\n",
      "\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[1;32mreturn\u001b[0m \u001b[0mg\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mFile:\u001b[0m      c:\\users\\80726\\.conda\\envs\\chatgptglm\\lib\\site-packages\\filterpy\\stats\\stats.py\n",
      "\u001b[1;31mType:\u001b[0m      function"
     ]
    }
   ],
   "source": [
    "from filterpy.stats import gaussian\n",
    "gaussian??"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd5ed3ee",
   "metadata": {},
   "source": [
    "让我们绘制一个均值为 22 $(\\mu=22)$，方差为 4 $(\\sigma^2=4)$ 的高斯分布。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8861e31d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_gaussian_pdf(22, 4, mean_line=True, xlabel='$^{\\circ}C$');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49a96aa1",
   "metadata": {},
   "source": [
    "这条曲线*意味着什么*？假设我们有一个读数为 22°C 的温度计。没有温度计是完全准确的，因此我们预计每个读数都会略微偏离实际值。然而，一个名为 [*Central Limit Theorem（中心极限定理  ）*](https://en.wikipedia.org/wiki/Central_limit_theorem) 的定理指出，如果我们进行多次测量，则测量结果将呈正态分布。当我们查看此图表时，我们可以看到它与温度计在 22°C 的实际温度下读取特定值的概率成正比。\n",
    "\n",
    "回想一下，高斯分布是*连续的*。想象一条无限长的直线——你随机选择的点为 2 的概率是多少。显然是 0%，因为有无数种选择可供选择。正态分布也是如此；在上图中，*恰好* 2°C 的概率为 0%，因为读数可以采用无限数量的值。\n",
    "\n",
    "这条曲线是什么？这就是我们所说的*概率密度函数。*任何区域的曲线下面积都会为您提供这些值的概率。因此，例如，如果您计算 20 到 22 之间曲线下的面积，则所得面积将是温度读数介于这两个温度之间的概率。\n",
    "\n",
    "这是另一种理解它的方法。岩石或海绵的*密度*是多少？它是衡量有多少质量被压缩到给定空间中的量度。岩石致密，海绵则不那么致密。所以，如果你想知道一块石头有多重但没有秤，你可以用它的体积乘以它的密度。这会给你它的质量。实际上，大多数物体的密度都是不同的，所以你可以在岩石上对他的体积对局部密度进行积分（目的时获得质量）\n",
    "\n",
    "$$M = \\iiint_R p(x,y,z)\\, dV$$\n",
    "\n",
    "我们对*概率密度*做同样的事情。如果您想知道温度在 20°C 和 21°C 之间，您可以将上面的曲线从 20 积分到 21。如您所知，曲线的积分可以为您提供曲线下的面积。由于这是概率密度的曲线，所以密度的积分就是概率。\n",
    "\n",
    "温度正好是 22°C 的概率是多少？直观地说，0。这些是实数，22°C 与 22.00000000000017°C 的几率是无穷小的。从数学上讲，如果我们从 22 积分到 22，我们会得到什么？零。\n",
    "\n",
    "回想一下岩石，岩石上的一个点的重量是多少？一个无穷小的点必须没有重量。询问单个点的重量是没有意义的，（同样的）询问具有单个值的连续分布的概率是没有意义的。两者的答案显然都是零。\n",
    "\n",
    "在实践中，我们的传感器没有无限精度，因此 22°C 的读数意味着一个范围，例如 22 $\\pm$ 0.1°C，我们可以通过从 21.9 积分到 22.1 来计算该范围的概率。\n",
    "\n",
    "我们可以用贝叶斯（学派）术语或频率（学派）术语来考虑这一点。作为贝叶斯主义者，如果温度计读数正好是 22°C，那么我们的信念就用曲线来描述——我们认为实际（系统）温度接近 22°C 的信念非常高，而我们认为实际温度接近 18°C非常低。作为频率（学派），我们会说，如果我们在 22°C 下对一个系统进行 10 亿次温度测量，那么测量值的直方图将看起来像这条曲线。\n",
    "\n",
    "你如何计算概率或曲线下的面积？你对高斯方程进行积分（integrate）\n",
    "\n",
    "$$ \\int^{x_1}_{x_0}  \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{1}{2}{(x-\\mu)^2}/\\sigma^2 } dx$$\n",
    "\n",
    "这称为*累积概率分布*，通常缩写为*cdf*。\n",
    "\n",
    "我写了`filterpy.stats.norm_cdf` 来为你计算积分。 例如，我们可以计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "44e3c77e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cumulative probability of range 21.5 to 22.5 is 19.74%\n",
      "Cumulative probability of range 23.5 to 24.5 is 12.10%\n"
     ]
    }
   ],
   "source": [
    "from filterpy.stats import norm_cdf\n",
    "print('Cumulative probability of range 21.5 to 22.5 is {:.2f}%'.format(\n",
    "      norm_cdf((21.5, 22.5), 22,4)*100))\n",
    "print('Cumulative probability of range 23.5 to 24.5 is {:.2f}%'.format(\n",
    "      norm_cdf((23.5, 24.5), 22,4)*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc447871",
   "metadata": {},
   "source": [
    "平均值 ($\\mu$) 就是听起来的样子——所有可能概率的平均值。由于曲线的对称形状，它也是曲线的最高部分。温度计读数为 22°C，这就是我们使用的平均值。\n",
    "\n",
    "随机变量 $X$ 的正态分布的符号是 $X \\sim\\ \\mathcal{N}(\\mu,\\sigma^2)$ 其中 $\\sim$ 表示*根据*分布。这意味着我可以将温度计的温度读数表示为\n",
    "\n",
    "$$\\text{temp} \\sim \\mathcal{N}(22,4)$$\n",
    "\n",
    "这是一个极其重要的结果。高斯允许我只用两个数字捕获无限数量的可能值！使用值 $\\mu=22$ 和 $\\sigma^2=4$ 我可以计算任何范围内的测量分布。\n",
    "\n",
    "一些来源使用 $\\mathcal N (\\mu, \\sigma)$ 而不是 $\\mathcal N (\\mu, \\sigma^2)$。两者都可以，它们都是约定。如果您看到诸如 $\\mathcal{N}(22,4)$ 之类的术语，您需要记住使用的是哪种形式。在本书中，我总是使用 $\\mathcal N (\\mu, \\sigma^2)$，所以在这个例子中 $\\sigma=2$, $\\sigma^2=4$。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d7fa456",
   "metadata": {},
   "source": [
    "## Section 3.8： The Variance and Belief\n",
    "\n",
    "由于这是一个概率密度分布，因此要求曲线下的面积始终等于 1。 这应该很直观——曲线下的区域代表所有可能的结果，*某事*发生，而*某事发生*的概率为 1，因此密度总和必须为 1。 我们可以用一些代码自己证明这一点。 （如果你有数学倾向，将高斯方程从 $-\\infty$ 积分到 $\\infty$）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e7ea52c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(norm_cdf((-1e8, 1e8), mu=0, var=4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ef82d8b",
   "metadata": {},
   "source": [
    "这导致了一个重要的见解。 如果方差很小，则曲线将变窄。 这是因为方差是衡量样本与平均值相差多少*的度量。 要保持面积等于 1，曲线也必须很高。 另一方面，如果方差很大，则曲线会很宽，因此它也必须很短才能使面积等于 1。\n",
    "\n",
    "让我们用图形来看看。 我们将使用前面提到的“filterpy.stats.gaussian”，它可以采用单个值或值数组。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2ae6293a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24197072451914337\n",
      "[0.378 0.622]\n"
     ]
    }
   ],
   "source": [
    "from filterpy.stats import gaussian\n",
    "# gaussian??\n",
    "print(gaussian(x=3.0, mean=2.0, var=1))\n",
    "print(gaussian(x=[3.0, 2.0], mean=2.0, var=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b5da47e",
   "metadata": {},
   "source": [
    "默认情况下，“高斯”对输出进行归一化，从而将输出转换回概率分布。 使用参数`normed`来控制它。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a3b81eff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.242 0.399]\n"
     ]
    }
   ],
   "source": [
    "print(gaussian(x=[3.0, 2.0], mean=2.0, var=1, normed=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8d34fee",
   "metadata": {},
   "source": [
    "如果高斯未归一化，则称为*高斯函数*而不是*高斯分布*。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b129547f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(15, 30, 0.05)\n",
    "plt.plot(xs, gaussian(xs, 23, 0.2**2), label='$\\sigma^2=0.2^2$')\n",
    "plt.plot(xs, gaussian(xs, 23, .5**2), label='$\\sigma^2=0.5^2$', ls=':')\n",
    "plt.plot(xs, gaussian(xs, 23, 1**2), label='$\\sigma^2=1^2$', ls='--')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c6eb4a3",
   "metadata": {},
   "source": [
    "这告诉我们什么？ $\\sigma^2=0.2^2$ 的高斯分布非常窄。就是说我们相信 $x=23$，并且我们对此非常确定：在 $\\pm 0.2$ 标准内。相比之下，$\\sigma^2=1^2$ 的高斯也相信 $x=23$，但我们对此不太确定。我们认为 $x=23$ 较低，因此我们对 $x$ 的可能值的信念是分散的——例如，我们认为 $x=20$ 或 $x=26$ 的可能性很大。 $\\sigma^2=0.2^2$ 几乎完全消除了 $22$ 或 $24$ 作为可能值，而 $\\sigma^2=1^2$ 认为它们几乎与 $23$ 一样可能。\n",
    "\n",
    "如果我们回想温度计，我们可以将这三条曲线视为代表三个不同温度计的读数。 $\\sigma^2=0.2^2$ 的曲线表示非常准确的温度计，$\\sigma^2=1^2$ 的曲线表示相当不准确的温度计。请注意高斯分布为我们提供的非常强大的属性——我们可以完全用两个数字来表示温度计的读数和误差——均值和方差。\n",
    "\n",
    "高斯的等价形式是 $\\mathcal{N}(\\mu,1/\\tau)$，其中 $\\mu$ 是 *mean* 而 $\\tau$ 是 *precision*。 $1/\\tau = \\sigma^2$;它是方差的倒数。虽然我们在本书中没有使用这个公式，但它强调了方差是衡量我们数据精确程度的指标。小的方差产生大的精度——我们的测量非常精确。相反，较大的方差会产生较低的精度——我们的信念分布在大范围内。你应该习惯于以这些等价形式思考高斯。在贝叶斯术语中，高斯反映了我们对测量的*信念*，它们表达了测量的*精度*，它们表达了测量中*方差*的大小。这些都是陈述同一事实的不同方式。\n",
    "\n",
    "我有点超前了，但是在接下来的章节中，我们将使用高斯函数来表达我们对诸如我们正在跟踪的物体的估计位置或我们正在使用的传感器的准确性等事物的信念。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78c015bb",
   "metadata": {},
   "source": [
    "## Section 3.9 The  68-95-99.7 Rule\n",
    "\n",
    "现在让我们讨论一下标准差。标准差是衡量数据偏离平均值的程度。对于高斯分布，68% 的数据在均值的一个标准差 ($\\pm1\\sigma$) 内，95% 在两个标准差 ($\\pm2\\sigma$) 内，99.7% 在三个标准差 ($ \\pm3\\sigma$)。这通常被称为 [68-95-99.7 规则](https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule)。如果你被告知一个班级的平均考试成绩为 71，标准差为 9.4，你可以得出结论，如果分布是正态的，95% 的学生得到的分数在 52.2 到 89.8 之间（即用 $71 (2 * 9.4)$)。\n",
    "\n",
    "最后，这些不是任意数字。如果我们位置的高斯是 $\\mu=22$ 米，那么标准差的单位也是米。因此 $\\sigma=0.2$ 意味着 68% 的测量范围在 21.8 到 22.2 米之间。方差是标准差的平方，因此 $\\sigma^2 = .04$ 米$^2$。正如您在上一节中看到的那样，编写 $\\sigma^2 = 0.2^2$ 可以使这更有意义，因为 0.2 与数据的单位相同。\n",
    "\n",
    "下图描述了标准偏差和正态分布之间的关系。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "79cd9519",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.gaussian_internal import display_stddev_plot\n",
    "display_stddev_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a2296ae",
   "metadata": {},
   "source": [
    "## Section 3.10：交互式高斯 --Interactive Gaussians\n",
    "\n",
    "对于那些在 Jupyter Notebook 中阅读此内容的人，这里是高斯图的交互式版本。 使用滑块修改 $\\mu$ 和 $\\sigma^2$。 调整 $\\mu$ 会使图形左右移动，因为您是在调整均值，而调整 $\\sigma^2$ 会使钟形曲线变粗变细。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "4049ad74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "93dcb8d18c53427eb9a417cee0fe2fe3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=5.0, description='mu', max=7.0, min=3.0), FloatSlider(value=0.03, desc…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "from ipywidgets import interact, FloatSlider\n",
    "import matplotlib.pyplot as plt\n",
    "def plt_g(mu,variance):\n",
    "    plt.figure()\n",
    "    xs = np.arange(2, 8, 0.01)\n",
    "    ys = gaussian(xs, mu, variance)\n",
    "    plt.plot(xs, ys)\n",
    "    plt.ylim(0, 0.04)\n",
    "\n",
    "interact(plt_g, mu=FloatSlider(value=5, min=3, max=7),\n",
    "         variance=FloatSlider(value = .03, min=.01, max=1.));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af718a1a",
   "metadata": {},
   "source": [
    "最后，如果你在网上阅读这篇文章，这里有一个高斯动画。 首先，平均值向右移动。 然后均值以 $\\mu=5$ 为中心并修改方差。\n",
    "<img src='animations/04_gaussian_animate.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69d38aa6",
   "metadata": {},
   "source": [
    "## Section 3.11: Computational Properties of Gaussians\n",
    "\n",
    "\n",
    "离散贝叶斯滤波器通过将任意概率分布相乘和相加来工作。 卡尔曼滤波器使用高斯而不是任意分布，但算法的其余部分保持不变。 这意味着我们将需要在高斯分布上进行乘法和加法。\n",
    "\n",
    "高斯的一个显着特性是两个独立的高斯分布和（https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables）也是高斯分布的！ 二者乘积（两个高斯分布的乘积）不是高斯的，而是与高斯成正比的。 在那里，我们可以说将两个高斯分布相乘的结果是一个高斯函数（在这种情况下，召回函数意味着不能保证值总和为 1 的性质，概率和为1）。\n",
    "\n",
    "在我们做数学之前，让我们直观地测试一下。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "446d1d7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-1, 3, 0.01)\n",
    "g1 = gaussian(x, mean=0.8, var=.1)\n",
    "g2 = gaussian(x, mean=1.3, var=.2)\n",
    "plt.plot(x, g1, x, g2)\n",
    "\n",
    "g = g1 * g2  # element-wise multiplication\n",
    "g = g / sum(g)  # normalize \n",
    "plt.plot(x, g, ls='-.');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e946b4a",
   "metadata": {},
   "source": [
    "在这里，我创建了两个高斯函数 g1=$\\mathcal N(0.8, 0.1)$ 和 g2=$\\mathcal N(1.3, 0.2)$ 并绘制了它们。 然后我将它们相乘并将结果归一化。 如您所见，结果*看起来*像高斯分布。\n",
    "\n",
    "高斯函数是非线性函数。 通常，如果您将非线性方程相乘，您最终会得到不同类型的函数。 例如，将两个 sin 相乘的形状与`sin(x)` 非常不同。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "8fa2ca9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 4*np.pi, 0.01)\n",
    "plt.plot(np.sin(1.2*x))\n",
    "plt.plot(np.sin(1.2*x) * np.sin(2*x));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79e317a3",
   "metadata": {},
   "source": [
    "但是两个高斯分布相乘的结果是一个高斯函数。 这是卡尔曼滤波器在计算上可行的关键原因。 换句话说，卡尔曼滤波器使用高斯*因为*它们在计算上很好。\n",
    "\n",
    "两个独立高斯分布的乘积由下式给出：\n",
    "\n",
    "$$\\begin{aligned}\\mu &=\\frac{\\sigma_1^2\\mu_2 + \\sigma_2^2\\mu_1}{\\sigma_1^2+\\sigma_2^2}\\\\\n",
    "\\sigma^2 &=\\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} \n",
    "\\end{aligned}$$\n",
    "\n",
    "两个高斯分布的和由下式给出\n",
    "\n",
    "$$\\begin{gathered}\\mu = \\mu_1 + \\mu_2 \\\\\n",
    "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n",
    "\\end{gathered}$$\n",
    "\n",
    "在本章的最后，我推导出这些方程。 然而，理解推导并不是很重要。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60c4543d",
   "metadata": {},
   "source": [
    "## Section 3.12 Putting it all Together\n",
    "\n",
    "现在我们准备讨论如何在滤波中使用高斯分布。 在下一章中，我们将使用 Gaussins 实现一个滤波器。 在这里，我将解释为什么我们要使用高斯。\n",
    "\n",
    "在上一章中，我们用数组表示概率分布。 我们通过计算该分布与另一个分布的元素乘积来执行更新计算，该分布表示每个点测量的似然，如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "804e4d4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def normalize(p):\n",
    "    return p / sum(p)\n",
    "\n",
    "def update(likelihood, prior):\n",
    "    return normalize(likelihood * prior)\n",
    "\n",
    "prior =  normalize(np.array([4, 2, 0, 7, 2, 12, 35, 20, 3, 2]))\n",
    "plt.subplot(311)\n",
    "book_plots.bar_plot(prior)\n",
    "likelihood = normalize(np.array([3, 4, 1, 4, 2, 38, 20, 18, 1, 16]))\n",
    "plt.subplot(312)\n",
    "book_plots.bar_plot(likelihood)\n",
    "posterior = update(likelihood, prior)\n",
    "plt.subplot(313)\n",
    "book_plots.bar_plot(posterior)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b620707e",
   "metadata": {},
   "source": [
    "换句话说，我们必须计算 10 次乘法才能得到这个结果。 对于具有多维大型数组的真实滤波器，我们需要数十亿次乘法和大量内存。\n",
    "\n",
    "但是这个分布看起来像一个高斯分布。 如果我们使用高斯分布而不是数组怎么办？ 我将计算后验的均值和方差，并将其绘制在条形图上。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "fe9368d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: 5.88 var: 1.24\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(0, 10, .01)\n",
    "\n",
    "def mean_var(p):\n",
    "    x = np.arange(len(p))\n",
    "    mean = np.sum(p * x,dtype=float)\n",
    "    var = np.sum((x - mean)**2 * p)\n",
    "    return mean, var\n",
    "\n",
    "mean, var = mean_var(posterior)\n",
    "book_plots.bar_plot(posterior)\n",
    "plt.plot(xs, gaussian(xs, mean, var, normed=False), c='r');\n",
    "print('mean: %.2f' % mean, 'var: %.2f' % var)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fed86d9",
   "metadata": {},
   "source": [
    "这令人印象深刻。 我们可以只用两个数字来描述数字的整个分布。 也许这个例子没有说服力，因为分布中只有 10 个数字。 但是一个真正的问题可能有数百万个数字，但仍然只需要两个数字来描述它。\n",
    "\n",
    "接下来，回想一下我们的滤波器实现的 Update 函数\n",
    "\n",
    "```python\n",
    "def update(likelihood, prior):\n",
    "    return normalize(likelihood * prior)\n",
    "```\n",
    "\n",
    "如果数组包含一百万个元素，那就是一百万次乘法。 但是，如果我们用高斯分布替换数组，那么我们将执行该计算\n",
    "\n",
    "$$\\begin{aligned}\\mu &=\\frac{\\sigma_1^2\\mu_2 + \\sigma_2^2\\mu_1}{\\sigma_1^2+\\sigma_2^2}\\\\\n",
    "\\sigma^2 &=\\frac{\\sigma_1^2\\sigma_2^2}{\\sigma_1^2+\\sigma_2^2} \n",
    "\\end{aligned}$$\n",
    "\n",
    "这是三个乘法和两个除法。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89218600",
   "metadata": {},
   "source": [
    "### Section 3.12.1 Bayes Theorem\n",
    "\n",
    "在上一章中，在上一章中，我们开发了一种算法，通过推理在每个时刻所拥有的信息，我们将其表示为离散概率分布。 在这个过程中，我们发现了 [*Bayes' Theorem*](https://en.wikipedia.org/wiki/Bayes%27_theorem)。 贝叶斯定理告诉我们如何在给定先验信息的情况下计算事件的概率。\n",
    "\n",
    "我们用这个概率计算实现了 `update()` 函数：\n",
    "\n",
    "$$ \\mathtt{posterior} = \\frac{\\mathtt{likelihood}\\times \\mathtt{prior}}{\\mathtt{normalization}}$$ \n",
    "\n",
    "事实证明，这就是贝叶斯定理。 稍后我将发展数学，但在许多方面会掩盖这个等式中表达的简单概念。 我们将其解读为：\n",
    "\n",
    "$$ updated\\,knowledge = \\big\\|likelihood\\,of\\,new\\,knowledge\\times prior\\, knowledge \\big\\|$$\n",
    "\n",
    "其中$\\| \\cdot\\|$ 表示对术语进行归一化。\n",
    "\n",
    "我们通过狗在走廊上行走的简单案例说明贝叶斯定理的两个过程。 然而，正如我们将看到的，同样的等式适用于一系列滤波问题。 我们将在随后的每一章中使用这个等式。\n",
    "\n",
    "\n",
    "回顾一下，*先验*是在我们包含测量概率（*似然（likelihood）*）之前发生某事的概率，*后验*是我们在结合测量信息后计算的概率。\n",
    "\n",
    "贝叶斯定理是\n",
    "\n",
    "$$P(A \\mid B) = \\frac{P(B \\mid A)\\, P(A)}{P(B)}$$\n",
    "\n",
    "$P(A \\mid B)$ 被称为 [*条件概率*](https://en.wikipedia.org/wiki/Conditional_probability)。 也就是说，它表示 $A$ 发生的概率 *if* $B$ 发生。 例如，如果昨天也下雨，那么今天比典型的一天更有可能下雨，因为降雨系统通常持续一天以上。 鉴于昨天下雨，我们将今天下雨的概率写为 $P$(今天下雨 $\\mid$ 昨天下雨)。\n",
    "\n",
    "\n",
    "我掩盖了一个重要的观点。 在我们上面的代码中，我们使用的不是单个概率，而是一个概率数组——一个*概率分布*。 我刚刚给出的贝叶斯方程使用的是概率，而不是概率分布。 然而，它同样适用于概率分布。 我们对概率分布使用小写 $p$\n",
    "\n",
    "\n",
    "$$p(A \\mid B) = \\frac{p(B \\mid A)\\, p(A)}{p(B)}$$\n",
    "\n",
    "在上面的等式中，$B$ 是*证据（evidence）*，$p(A)$ 是*先验*，$p(B \\mid A)$ 是*似然*，$p(A \\mid B)$ 是*后验*。 通过用相应的单词替换数学术语，您可以看到贝叶斯定理与我们的更新方程匹配。 让我们根据我们的问题重写方程。 我们将使用 $x_i$ 表示 *i* 处的位置，并使用 $z$ 进行测量。 因此，我们想知道 $P(x_i \\mid z)$，即在给定测量 $z$ 的情况下，狗在 $x_i$ 处的概率。\n",
    "\n",
    "因此，让我们将其代入方程并求解。\n",
    "\n",
    "$$p(x_i \\mid z) = \\frac{p(z \\mid x_i) p(x_i)}{p(z)}$$\n",
    "\n",
    "这看起来很难看，但实际上很简单。 让我们弄清楚右边每个术语的含义。 首先是$p(z \\mid x_i)$ ，称为似然，或者称为在每个单元 $x_i$ 处测量的概率。 $p(x_i)$ 是 *prior* - 我们在合并测量之前的信念。 我们将它们相乘。 这只是 `update()` 函数中的未归一化前进行的乘法：\n",
    "\n",
    "```python\n",
    "def update(likelihood, prior):\n",
    "    posterior = prior * likelihood   # p(z|x) * p(x)\n",
    "    return normalize(posterior)\n",
    "```\n",
    "\n",
    "最后要考虑的项是分母 $p(z)$。 这是在不考虑位置的情况下获得测量值 $z$ 的概率。 它通常被称为*证据（evidence）*。 我们在代码中通过对 $x$ 求和或“sum(belief)”（信念求和）来计算它。 这就是我们计算归一化的方式！ 因此，`update()` 函数只不过是计算贝叶斯定理。\n",
    "\n",
    "文献经常以积分的形式给你这些方程。 毕竟，积分只是对连续函数的求和。 所以，你可能会看到贝叶斯定理写成\n",
    "\n",
    "$$p(A \\mid B) = \\frac{p(B \\mid A)\\, p(A)}{\\int p(B \\mid A_j) p(A_j) \\,\\, \\mathtt{d}A_j}\\cdot$$\n",
    "\n",
    "这个分母通常无法（求得）解析解；使用数学手段对其进行显式求解是非常困难的。最近的[意见书]（http://www.statslife.org.uk/opinion/2405-we-need-to-rethink-how-we-teach-statistics-from-the-ground-up）统计学会称其为“狗的早餐”[8]。采用贝叶斯方法的滤波教科书充满了没有解析解的积分方程。不要被这些方程吓倒，因为我们通过归一化我们的后验来简单地处理这个积分。我们将在 **粒子滤波器（Particle Filters）** 一章中学习更多处理此问题的技术。在那之前，要认识到在实践中它只是一个我们可以进行求和的标准化项（归一化项）。我想说的是，当您面对一页积分时，只需将它们视为总和，并将它们与本章联系起来，通常困难就会消失。问问自己“为什么我们要对这些值求和”，以及“我为什么要除以这一项”。令人惊讶的是，答案往往显而易见。令人惊讶的是，作者常常忽略了这种解释。\n",
    "\n",
    "贝叶斯定理的强度可能对你来说还不是很明显。我们要计算 $p(x_i \\mid Z)$。也就是说，在第 i 步，给定测量结果我们的可能状态是什么。总的来说，这是一个非常困难的问题。贝叶斯定理是通用的。我们可能想知道根据癌症检测结果我们患癌症的概率，或者在给定各种传感器读数的情况下下雨的概率。表示问题似乎无法解决。\n",
    "\n",
    "但是贝叶斯定理让我们可以使用逆 $p(Z\\mid x_i)$ 来计算它，这通常很容易计算\n",
    "\n",
    "$$p(x_i \\mid Z) \\propto p(Z\\mid x_i)\\, p(x_i)$$\n",
    "\n",
    "也就是说，要计算在给定特定传感器读数的情况下下雨的可能性，我们只需要计算给定正在下雨的传感器读数的可能性！ 这是一个***容易得多***的问题！ 好吧，天气预报仍然是一个难题，但贝叶斯使它变得容易处理。\n",
    "\n",
    "同样，正如您在离散贝叶斯一章中看到的那样，我们通过计算传感器读数在西蒙位于位置“x”的可能性来计算西蒙在走廊的任何给定部分的可能性。 一个难题变得容易。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8138eada",
   "metadata": {},
   "source": [
    "### Section 3.12.2 Total Probability Theorem\n",
    "\n",
    "我们现在知道了 `update()` 函数背后的形式数学； `predict()` 函数呢？ `predict()` 实现了[*全概率定理（total probability theorem）*]（https://en.wikipedia.org/wiki/Law_of_total_probability）。让我们回顾一下 `predict()` 的计算结果。它计算在给定所有可能运动事件的概率的情况下处于任意给定位置的概率。让我们将其表示为等式。在时间 $t$ 处于位置 $i$ 的概率可以写成 $P(X_i^t)$。我们将其计算为在时间 $t-1$的**先验概率** $P(X_j^{t-1})$ 乘以从（cell） $x_j$ 移动到 $x_i$ 的总和（类似于第二章的卷积）。那是\n",
    "\n",
    "$$P(X_i^t) = \\sum_j P(X_j^{t-1}) P(x_i | x_j)$$\n",
    "\n",
    "该等式称为*全概率定理*。引用维基百科 [6] “它表达了可以通过几个不同事件实现的结果的总概率”。我本可以给你这个方程并实现“predict()”，但是你理解这个方程为什么起作用的机会很小。提醒一下，这里是计算这个方程的代码\n",
    "\n",
    "\n",
    "```python\n",
    "for i in range(N):\n",
    "    for k in range (kN):\n",
    "        index = (i + (width-k) - offset) % N\n",
    "        result[i] += prob_dist[index] * kernel[k]\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5352db8d",
   "metadata": {},
   "source": [
    "## Section3.13 Computing Probabilities with scipy.stats\n",
    "\n",
    "在本章中，我使用了来自 [FilterPy](https://github.com/rlabbe/filterpy) 的代码来计算和绘制高斯分布图。 我这样做是为了让您有机会查看代码并了解这些功能是如何实现的。 然而，Python 自带“电池（batteries included）”，它在模块`scipy.stats` 中提供了广泛的统计功能。 那么让我们来看看如何使用 scipy.stats 来计算统计数据和概率。\n",
    "\n",
    "`scipy.stats` 模块包含许多对象，您可以使用它们来计算各种概率分布的属性。 该模块的完整文档在这里：http://docs.scipy.org/doc/scipy/reference/stats.html。 我们将关注实现正态分布的norm。 让我们看一些使用`scipy.stats.norm`计算高斯的代码，并将其值与FilterPy的`gaussian()`函数返回的值进行比较。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e2bf5b1e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.13114657203397997\n",
      "0.13114657203397995\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "import filterpy.stats\n",
    "print(norm(2, 3).pdf(1.5))\n",
    "print(filterpy.stats.gaussian(x=1.5, mean=2, var=3*3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88dc9731",
   "metadata": {},
   "source": [
    "调用“norm(2, 3)”创建了 scipy 所谓的“冻结（frozen）”分布——它创建并返回一个平均值为 2、标准差为 3 的对象。然后您可以多次使用该对象来获得概率 各种值的密度，如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "30cf728a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdf of 1.5 is       0.1311\n",
      "pdf of 2.5 is also  0.1311\n",
      "pdf of 2 is         0.1330\n"
     ]
    }
   ],
   "source": [
    "n23 = norm(2, 3)\n",
    "print('pdf of 1.5 is       %.4f' % n23.pdf(1.5))\n",
    "print('pdf of 2.5 is also  %.4f' % n23.pdf(2.5))\n",
    "print('pdf of 2 is         %.4f' % n23.pdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39b22e4c",
   "metadata": {},
   "source": [
    "[scipy.stats.norm](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.normfor) [2] 的文档列出了许多其他功能 . 例如，我们可以使用 rvs() 函数从分布中生成 $n$ 个样本。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "62273309",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.118  8.514 -0.584  2.669  1.093  1.055  2.882\n",
      "  5.617  1.919 -0.655  1.278 -2.832  0.915 -3.146\n",
      "  2.119]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(precision=3, linewidth=50)\n",
    "print(n23.rvs(size=15))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7393ae9c",
   "metadata": {},
   "source": [
    "我们可以得到[*累积分布函数（CDF）*]（https://en.wikipedia.org/wiki/Cumulative_distribution_function） ，它是从分布中随机抽取的值小于或等于$x$的概率。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "4d730f3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5\n"
     ]
    }
   ],
   "source": [
    "# probability that a random value is less than the mean 2\n",
    "print(n23.cdf(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8055590f",
   "metadata": {},
   "source": [
    "我们可以得到分布的各种性质："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "86645b6f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variance is 9.0\n",
      "standard deviation is 3.0\n",
      "mean is 2.0\n"
     ]
    }
   ],
   "source": [
    "print('variance is', n23.var())\n",
    "print('standard deviation is', n23.std())\n",
    "print('mean is', n23.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac9bdf9c",
   "metadata": {},
   "source": [
    "## Section 3.15 Limitations of Using Gaussians to Model the World\n",
    "\n",
    "前面我提到了*中心极限定理*，它指出在某些条件下，任何独立随机变量的算术和都将呈正态分布，而不管随机变量如何分布。这对我们很重要，因为自然界充满了非正态分布，但是当我们将中心极限定理应用于大量人口时，我们最终会得到正态分布。\n",
    "\n",
    "然而，证明的一个关键部分是“在某些条件下”。这些条件通常不适用于物理世界。例如，厨房秤的读数不能低于零，但如果我们将测量误差表示为高斯曲线，则曲线左侧延伸到负无穷大，这意味着给出负读数的可能性非常小。\n",
    "\n",
    "这是一个广泛的话题，我不会详尽地讨论。\n",
    "\n",
    "让我们考虑一个简单的例子。我们认为考试成绩是正态分布的。你曾经遇到过一个教授“按曲线打分”，你一直受制于这个假设。但当然，考试成绩不能服从正态分布。这是因为无论离均值有多远，该分布都为任何值分配了非零概率分布。因此，例如，假设您的平均值为 90，标准差为 13。正态分布假设某人得到 90 的可能性很大，而某人得到 40 的可能性很小。但是，这也意味着存在是某人获得 -10 或 150 分的可能性很小。它分配了极小的机会获得 $-10^{300}$ 或 $10^{32986}$ 的分数。高斯分布的尾部是无限长的。\n",
    "\n",
    "但是对于测试，我们知道这是不正确的。忽略额外的学分，你不能得到小于 0 或大于 100 的分数。让我们使用正态分布绘制这个值范围，看看这代表真实考试分数分布有多差。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "3a4fcd27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(10, 100, 0.05)\n",
    "ys = [gaussian(x, 90, 30) for x in xs]\n",
    "plt.plot(xs, ys, label='var=0.2')\n",
    "plt.xlim(0, 120)\n",
    "plt.ylim(-0.02, 0.09);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f4b0e2e",
   "metadata": {},
   "source": [
    "曲线下的面积不能等于 1，因此它不是概率分布。实际发生的情况是，比正态分布预测的更多学生获得的分数接近范围的上限（例如），并且尾巴变得“胖”。此外，该测试可能无法完美区分学生技能的微小差异，因此平均值左侧的分布也可能在某些地方有点聚集。\n",
    "\n",
    "传感器测量世界。传感器测量中的误差很少是真正的高斯误差。现在谈论这给卡尔曼滤波器设计者带来的困难还为时过早。值得牢记的是，卡尔曼滤波器数学是基于理想化的世界模型。现在我将介绍一些代码，我将在本书后面使用这些代码来形成分布以模拟各种过程和传感器。这种分布称为 [*Student's $t$-distribution*](https://en.wikipedia.org/wiki/Student%27s_t-distribution)。\n",
    "\n",
    "假设我想对输出中有一些白噪声的传感器进行建模。为简单起见，假设信号为常数 10，噪声的标准差为 2。我们可以使用函数 `numpy.random.randn()` 获得均值为 0 和标准差的随机数1. 我可以用以下方法模拟这个："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "a1a69a5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "def sense():\n",
    "    return 10 + randn()*2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dc24d2b",
   "metadata": {},
   "source": [
    "让我们绘制那个信号，看看它是什么样子的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "34d9f063",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = [sense() for i in range(5000)]\n",
    "plt.plot(zs, lw=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13a1ef2e",
   "metadata": {},
   "source": [
    "这看起来就像我所期望的那样。 信号以 10 为中心。标准偏差为 2 意味着 68% 的测量值在 10 的 $\\pm$ 2 内，99% 的测量值在 10 的 $\\pm$ 6 内，看起来像 正在发生。\n",
    "\n",
    "现在让我们看看使用 Student 的 $t$-distribution 生成的分布。 我不会深入数学，只是给你它的源代码，然后使用它绘制一个分布。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "a5621142",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import math\n",
    "\n",
    "def rand_student_t(df, mu=0, std=1):\n",
    "    \"\"\"return random number distributed by Student's t \n",
    "    distribution with `df` degrees of freedom with the \n",
    "    specified mean and standard deviation.具有' df '自由度，具有指定的平均值和标准差。\n",
    "    \"\"\"\n",
    "    x = random.gauss(0, std)\n",
    "    y = 2.0*random.gammavariate(0.5*df, 2.0)\n",
    "    return x / (math.sqrt(y / df)) + mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d81c5cc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sense_t():\n",
    "    return 10 + rand_student_t(7)*2\n",
    "\n",
    "zs = [sense_t() for i in range(5000)]\n",
    "plt.plot(zs, lw=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f79c9d6",
   "metadata": {},
   "source": [
    "从图中我们可以看出，虽然输出与正态分布相似，但仍有离群值远远超过平均值 3 个标准差（7 到 13）的异常值。\n",
    "\n",
    "学生的 $t$ 分布不太可能是您的传感器（例如 GPS 或多普勒）如何执行的准确模型，而且这不是一本关于如何为物理系统建模的书。但是，当出现真实世界的噪声时，它确实会产生合理的数据来测试您的滤波器的性能。我们将在本书其余部分的模拟和测试中使用类似的分布。\n",
    "\n",
    "**注：也就是说这个student's t-distribution 不类似实际传感器的模型，但是用它产生的数据，可以测试滤波器的性能**\n",
    "\n",
    "这不是一个无所事事的问题。卡尔曼滤波器方程假设噪声是正态分布的，如果这不是真的，则执行次优。任务关键型滤波器（例如航天器上的滤波器）的设计人员需要掌握大量有关航天器上传感器性能的理论和经验知识。例如，我在 NASA 任务中看到的一个演示文稿指出，虽然理论上他们应该使用 3 个标准偏差来区分实际测量中的噪声，但他们必须使用 5 到 6 个标准偏差。这是他们通过实验确定的。\n",
    "\n",
    "rand_student_t 的代码包含在 `filterpy.stats` 中。您可以将它与\n",
    "\n",
    "```python\n",
    "from filterpy.stats import rand_student_t\n",
    "```\n",
    "\n",
    "虽然我不会在这里介绍它，但统计学已经定义了描述概率分布形状的方法，即概率分布与指数分布的变化方式。 正态分布围绕均值对称形成 - 就像钟形曲线。 但是，概率分布可能围绕均值不对称。 对此的度量称为 [*skew*](https://en.wikipedia.org/wiki/Skewness)。 尾部可以缩短、变胖、变细或以其他方式与指数分布不同的形状。 对此的度量称为 [*kurtosis*](https://en.wikipedia.org/wiki/Kurtosis)。 `scipy.stats` 模块包含计算这些统计数据的函数 `describe` 等等。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "347102c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DescribeResult(nobs=5000, minmax=(1.015739032360507, 18.913183437899463), mean=9.981733806493002, variance=2.814899623973014, skewness=0.08559744451314176, kurtosis=1.768511800835456)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy\n",
    "scipy.stats.describe(zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "393774ab",
   "metadata": {},
   "source": [
    "让我们检查两个正常人群，一是小规模，另一个是大规模："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "0eae9e5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DescribeResult(nobs=10, minmax=(-1.6652727959066043, 0.5858180173310898), mean=-0.2330724289920519, variance=0.48357267972828943, skewness=-0.7036393862480442, kurtosis=-0.2118206546355741)\n",
      "\n",
      "DescribeResult(nobs=300000, minmax=(-4.419114461886653, 4.936273036403739), mean=-0.0008057696034383672, variance=0.9993138432805311, skewness=0.0028386105596951757, kurtosis=-0.009872411580244655)\n"
     ]
    }
   ],
   "source": [
    "print(scipy.stats.describe(np.random.randn(10)))\n",
    "print()\n",
    "print(scipy.stats.describe(np.random.randn(300000)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91eb5437",
   "metadata": {},
   "source": [
    "小样本具有非零的skew和kurtosis，因为少量样本没有很好地分布在均值 0 周围。您还可以通过将计算的均值和方差与理论均值 0 和方差 1 进行比较来看到这一点。 比较大样本的均值和方差非常接近理论值，偏度和峰度都接近于零。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aee9caa",
   "metadata": {},
   "source": [
    "## Section 3.15 Product of Gaussians (Optional)\n",
    "\n",
    "\n",
    "阅读本节并不重要。 在这里，我推导出两个高斯乘积的方程。\n",
    "\n",
    "您可以通过将两个高斯方程相乘并组合项来找到此结果。 代数上有点棘手。 我将使用贝叶斯定理推导出它。 我们可以将问题表述为：设先验为$N(\\bar\\mu, \\bar\\sigma^2)$，测量为$z \\propto N(z, \\sigma_z^2)$。 给定测量 z 的后验 x 是多少？\n",
    "\n",
    "将后验写为 $p(x \\mid z)$。 现在我们可以使用贝叶斯定理来说明\n",
    "\n",
    "$$p(x \\mid z) = \\frac{p(z \\mid x)p(x)}{p(z)}$$\n",
    "\n",
    "$p(z)$ 是一个归一化常数，所以我们可以创建一个正比项\n",
    "\n",
    "$$p(x \\mid z) \\propto p(z|x)p(x)$$\n",
    "\n",
    "现在我们将方程代入高斯方程，即\n",
    "\n",
    "$$p(z \\mid x) = \\frac{1}{\\sqrt{2\\pi\\sigma_z^2}}\\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]$$\n",
    "\n",
    "$$p(x) = \\frac{1}{\\sqrt{2\\pi\\bar\\sigma^2}}\\exp \\Big[-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big]$$\n",
    "\n",
    "我们可以去掉前面的（系数）项，因为它们是常数，给我们\n",
    "\n",
    "$$\\begin{aligned}\n",
    "p(x \\mid z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big]\\\\\n",
    "&\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}-\\frac{(x-\\bar\\mu)^2}{2\\bar\\sigma^2}\\Big] \\\\\n",
    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[\\bar\\sigma^2(z-x)^2+\\sigma_z^2(x-\\bar\\mu)^2]\\Big]\n",
    "\\end{aligned}$$\n",
    "\n",
    "现在我们根据后验 $x$ 乘以平方项和组。\n",
    "\n",
    "$$\\begin{aligned}\n",
    "p(x \\mid z) &\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[\\bar\\sigma^2(z^2 -2xz + x^2) + \\sigma_z^2(x^2 - 2x\\bar\\mu+\\bar\\mu^2)]\\Big ] \\\\\n",
    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\bar\\sigma^2}[x^2(\\bar\\sigma^2+\\sigma_z^2)-2x(\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z) + (\\bar\\sigma^2z^2+\\sigma_z^2\\bar\\mu^2)]\\Big ]\n",
    "\\end{aligned}$$\n",
    "\n",
    "最后的括号不包含后验 $x$，因此可以将其视为常量并丢弃。\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2(\\bar\\sigma^2+\\sigma_z^2)-2x(\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z)}{\\sigma_z^2\\bar\\sigma^2}\\Big ]\n",
    "$$\n",
    "\n",
    "分子和分母除以$\\bar\\sigma^2+\\sigma_z^2$得到\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2-2x(\\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2})}{\\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}}\\Big ]\n",
    "$$\n",
    "\n",
    "比例性允许我们随意创建或删除常量，因此我们可以将其考虑在内（配方，除了一项）\n",
    "\n",
    "$$p(x \\mid z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{(x-\\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2})^2}{\\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}}\\Big ]\n",
    "$$\n",
    "\n",
    "高斯是\n",
    "\n",
    "$$N(\\mu,\\, \\sigma^2) \\propto \\exp\\Big [-\\frac{1}{2}\\frac{(x - \\mu)^2}{\\sigma^2}\\Big ]$$\n",
    "\n",
    "所以我们可以看到 $p(x \\mid z)$ 的平均值为\n",
    "\n",
    "$$\\mu_\\mathtt{posterior} = \\frac{\\sigma_z^2\\bar\\mu + \\bar\\sigma^2z}{\\bar\\sigma^2+\\sigma_z^2}$$\n",
    "\n",
    "和方差\n",
    "\n",
    "$$\n",
    "\\sigma_\\mathtt{posterior} = \\frac{\\sigma_z^2\\bar\\sigma^2}{\\bar\\sigma^2+\\sigma_z^2}\n",
    "$$\n",
    "\n",
    "我已经删除了常数，因此结果不是正常的，而是与一成正比的。 贝叶斯定理使用 $p(z)$ 除数进行归一化，确保结果正常。 我们在滤波器的更新步骤中进行归一化，确保滤波器估计是高斯的。\n",
    "\n",
    "$$\\mathcal N_1 = \\| \\mathcal N_2\\cdot \\mathcal N_3\\|$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "361603a0",
   "metadata": {},
   "source": [
    "## Section 3.16 Sum of Gaussians (Optional)\n",
    "\n",
    "同样，这部分也不重要。 在这里，我推导出两个高斯之和的方程。\n",
    "\n",
    "两个高斯的和由下式给出\n",
    "\n",
    "$$\\begin{gathered}\\mu = \\mu_1 + \\mu_2 \\\\\n",
    "\\sigma^2 = \\sigma^2_1 + \\sigma^2_2\n",
    "\\end{gathered}$$\n",
    "\n",
    "有几个证明。 我将使用卷积，因为我们在上一章对概率直方图使用卷积。\n",
    "\n",
    "为了找到两个高斯随机变量之和的密度函数，我们将每个变量的密度函数相加。 它们是非线性的连续函数，因此我们需要用积分计算总和。 如果随机变量 $p$ 和 $z$（例如先验和测量）是独立的，我们可以用\n",
    "\n",
    "$$p(x) = \\int\\limits_{-\\infty}^\\infty f_p(x-z)f_z(z)\\, dx$$\n",
    "\n",
    "这是卷积的方程。 现在我们只做一些数学运算：\n",
    "\n",
    "$p(x) = \\int\\limits_{-\\infty}^\\infty f_2(x-x_1)f_1(x_1)\\, dx$\n",
    "\n",
    "$=  \\int\\limits_{-\\infty}^\\infty \n",
    "\\frac{1}{\\sqrt{2\\pi}\\sigma_z}\\exp\\left[-\\frac{(x - z - \\mu_z)^2}{2\\sigma^2_z}\\right]\n",
    "\\frac{1}{\\sqrt{2\\pi}\\sigma_p}\\exp\\left[-\\frac{(x - \\mu_p)^2}{2\\sigma^2_p}\\right] \\, dx$\n",
    "\n",
    "$=  \\int\\limits_{-\\infty}^\\infty\n",
    "\\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right]\n",
    "\\frac{1}{\\sqrt{2\\pi}\\frac{\\sigma_p\\sigma_z}{\\sqrt{\\sigma_p^2 + \\sigma_z^2}}} \\exp\\left[ -\\frac{(x - \\frac{\\sigma_p^2(x-\\mu_z) + \\sigma_z^2\\mu_p}{}))^2}{2\\left(\\frac{\\sigma_p\\sigma_x}{\\sqrt{\\sigma_z^2+\\sigma_p^2}}\\right)^2}\\right] \\, dx$\n",
    "\n",
    "$= \\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right] \\int\\limits_{-\\infty}^\\infty\n",
    "\\frac{1}{\\sqrt{2\\pi}\\frac{\\sigma_p\\sigma_z}{\\sqrt{\\sigma_p^2 + \\sigma_z^2}}} \\exp\\left[ -\\frac{(x - \\frac{\\sigma_p^2(x-\\mu_z) + \\sigma_z^2\\mu_p}{}))^2}{2\\left(\\frac{\\sigma_p\\sigma_x}{\\sqrt{\\sigma_z^2+\\sigma_p^2}}\\right)^2}\\right] \\, dx$\n",
    "\n",
    "积分内的表达式是正态分布。 正态分布的和为一，因此积分为一。 这给了我们\n",
    "\n",
    "$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right]$$\n",
    "\n",
    "这是一个正常的形式，其中\n",
    "\n",
    "$$\\begin{gathered}\\mu_x = \\mu_p + \\mu_z \\\\\n",
    "\\sigma_x^2 = \\sigma_z^2+\\sigma_p^2\\, \\square\\end{gathered}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be630050",
   "metadata": {},
   "source": [
    "## Summary and Key Points\n",
    "\n",
    "本章总体上对统计学的介绍很差。 在本书的其余部分中，我只介绍了使用高斯函数所需的概念，不再赘述。 如果您打算阅读卡尔曼滤波器文献，我所介绍的内容不会让您走得太远。 如果这对您来说是一个新话题，我建议您阅读统计教科书。 我一直很喜欢 Schaum 系列自学，而 Alan Downey 的 *Think Stats* [5] 也非常好，可以在线免费获得。\n",
    "\n",
    "在我们继续之前，您**必须**了解以下几点：\n",
    "\n",
    "* Normals表示连续概率分布\n",
    "* 它们完全由两个参数描述：均值 ( $\\mu$ ) 和方差 ($\\sigma^2$)\n",
    "* $\\mu$ 是所有可能值的平均值\n",
    "* 方差 $\\sigma^2$ 表示我们的测量值与平均值偏离程度\n",
    "* 标准差 ($\\sigma$) 是方差的平方根 ($\\sigma^2$)\n",
    "* 自然界中的许多事物都近似于正态分布，但数学并不完美。\n",
    "* 在滤波问题中，计算 $p(x\\mid z)$ 几乎是不可能的，但计算 $p(z\\mid x)$ 很简单。 贝叶斯让我们从后者计算前者。\n",
    "\n",
    "接下来的几章将使用高斯和贝叶斯定理来帮助执行滤波。 如上一节所述，有时高斯学派不能很好地描述世界。 本书的后半部分专门讨论即使在噪声或系统行为非常非高斯时也能正常工作的滤波器。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e671b01",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/Supporting_Notebooks/Computing_and_plotting_PDFs.ipynb\n",
    "\n",
    "[2] http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html\n",
    "\n",
    "[3] http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html\n",
    "\n",
    "[4] Huber, Peter J. *Robust Statistical Procedures*, Second Edition. Society for Industrial and Applied Mathematics, 1996.\n",
    "\n",
    "[5] Downey, Alan. *Think Stats*, Second Edition. O'Reilly Media.\n",
    "\n",
    "https://github.com/AllenDowney/ThinkStats2\n",
    "\n",
    "http://greenteapress.com/thinkstats/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcac988b",
   "metadata": {},
   "source": [
    "## Useful Wikipedia Links\n",
    "\n",
    "https://en.wikipedia.org/wiki/Probability_distribution\n",
    "\n",
    "https://en.wikipedia.org/wiki/Random_variable\n",
    "\n",
    "https://en.wikipedia.org/wiki/Sample_space\n",
    "\n",
    "https://en.wikipedia.org/wiki/Central_tendency\n",
    "\n",
    "https://en.wikipedia.org/wiki/Expected_value\n",
    "\n",
    "https://en.wikipedia.org/wiki/Standard_deviation\n",
    "\n",
    "https://en.wikipedia.org/wiki/Variance\n",
    "\n",
    "https://en.wikipedia.org/wiki/Probability_density_function\n",
    "\n",
    "https://en.wikipedia.org/wiki/Central_limit_theorem\n",
    "\n",
    "https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule\n",
    "\n",
    "https://en.wikipedia.org/wiki/Cumulative_distribution_function\n",
    "\n",
    "https://en.wikipedia.org/wiki/Skewness\n",
    "\n",
    "https://en.wikipedia.org/wiki/Kurtosis"
   ]
  }
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